Consider the differential equation
$${{dy} \over {dx}} = 4(x + 2) - y$$
For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler's method with a step-size of 0.2 is ________. (round off to one decimal place)
A set of observations of independent variable (x) and the corresponding dependent variable (y) is given below.
| x | 5 | 2 | 4 | 3 |
|---|---|---|---|---|
| y | 16 | 10 | 13 | 12 |
Based on the data, the coefficient a of the linear regression model
y = a + bx
is estimated as 6.1. The coefficient b is _________. (round off to one decimal place)
A horizontal force of P kN is applied to a homogeneous body of weight 25 kN, as shown in the figure. The coefficient of friction between the body and the floor is 0.3. Which of the following statements is/are correct?
The total hardness in raw water is 500 milligram per liter as CaCO3. The total hardness of this raw water, expressed in milligram equivalent per liter, is (Consider the atomic weights of Ca, C, and O as 40 g/mol, 12 g/mol, and 16 g/mol, respectively.)